Zero directional derivative In what directions is the derivative of ƒ(x, y) = (x2 - y2) / (x2 + y2) at P(1, 1) equal to zero?

Q: Derivative of f(x)=1+ 2x+3xy computed * O explicitly equal to 2+3x implicitly equal to 2+3x+3dy/dx O…

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Q: 3. Approximate the first order derivative of f(x)= x² + 2x at x = 3, using Forward, Backward and…

A: Formulas for differences are enclosed next page

Q: A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with…

A: As per bartleby guidelines we only give first three question answers.

Q: the derivative of f(y)=4sin^9(y

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Q: B) Derivative following functions by using chain rule method 1) y = 5u³- u? , 2x = 4u? 2) у %3D |1 ,…

A: Answer (1): Given that, y=5u3-u2, 2x=4u2 Suppose fgx Then, to find the derivative apply the chain…

Q: Using a Derivative Let f'(t) f(5).

A: Given that f'(t) <0 in the interval (2,8).

Q: f(x+Ax)- f(x) Using the first principle of derivative f'(x) = %3D Ax Ax-0 Differentiate: y 4x - 6

A: Derivative of the function

Q: Derivative of the function f (x) = tan x at x = n/4

A: Differentiating with respect to x, we get

Q: derivative of the fun x + 2 y = e y' = %3D

A: We are asked to find the derivatives of the function.

Q: Derivative of y = (x(1-x^2)^3)/((1+x^2)^1/2)

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Q: 4. Function y = sin x at the point with the abscissa x A. Point of Tangency B. The Gradient of the…

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Q: 1. Centered-difference formula for the second derivative with one independent variable x y (x + h) –…

A: Claim: y''(x) = y(x+h)-2y(x)+y(x-h)h2-h212y(4)(ς) It is known that y = (x-∆x) =y(x) -∆xy'(x)…

Q: derivative of y = x^2 ln tan^2 x

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Q: Find the derivative of the function. State the domain of the derivative. f(x) = [In(x)]6 f '(x) =…

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Q: Find the relative extrema, if any, of the function. Use the Second Derivative Test if applicable.…

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Q: Derivative of T Determine the derivative of 1. y = 100 cos 3x 2. y = 5 tan (6x - 1) 3. y = 12 cot…

A: "Kindly ask other parts in different question as per Bartleby rules." 1., 2. and 3. are solved here.…

Q: Q: Use the Second Derivative Test to classify the local extremes of the function f(x, y) =…

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Q: derivative of the firm's profit function is F'(x) = -0.03x2 + 3x - 100, where x > 0 is the output…

A: We will use the basic knowledge of functions and derivatives of functions to answer this question.…

Q: Implicit differentiation x^2+2y^2-4=0

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Q: Applications of Derivative: Tangent and Normal Line 1. For x3 + y3 = 6xy, find the point where…

A: The given equation is:x3+y3=6xyTo find the point where the tangent line is horizontal

Q: derivative of the firm's profit function is F'(x) = -0.03x2 + 3x - 100, where x 2 0 is the output…

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Q: II. Application of Derivatives 3. Find the tangent line to f (r) = (2– 4x²)° at z = 1.

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Q: 6. Using the limit defenition of the derivative, find the equation of the line tangent to the curve…

A: We have to find the slope of the tangent line at first.Then we find its equation.

Q: Applying the Second Derivative Test Find the critical points of f (x, y) = (x2 + y2)e-x and analyze…

A: We have to find the critical points off (x, y) = (x2 + y2)e-x and analyze them using the Second…

Q: Using chain rule evaluate the first derivative of y=x²(x+1)³.

A: We have to find first derivative of the function using chain rule: y=x2x+13 We know the formula of…

Q: 2. Equation of Tangent Line through Curve y = sin x + cos x At the abscissa point 2 A. Point of…

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Q: True of False: Derivative of (arctan(e^(-x^2))) = [-2xe^(-x^2)] / [1 + e^(-2x^2)] Show your…

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Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable. f(x) =…

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Q: valuate the second derivative of the function at the given point. Use a computer algebra system to…

A: h(x)=193x+13 , at the point 1,649

Q: Derivative of aresine Assume that y = sin x is a differentia- ble function of x. By differentiating…

A: Given: y=sin-1x

Q: total derivative of the function f(x, y

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Q: Il relative extrema of the function f(x) = x* - 4x2 +2 by using the Second Derivative here…

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Q: arctan x Suppose that f is differentiable at 0 and f(0) = 5. Find the derivative of at x = 0. f(x)

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Q: uous derivative. The table above gives values of fand its derivative for x=0 and x=4. If f (z) dz =…

A: Here we have ∫04f(x)dx=8 and  we have to calculate,  ∫04xf'(x)dx=?

Q: Q: Use the Second Derivative Test to classify the local extremes of the function f(x,y) =…

A: The Second Derivative Test:  Find the critical points of . that is the solution of the simultaneous…

Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable. (If an…

A: We need to find maxima and minima.

Q: ctivity 1. Find the 2nd derivative of the even-numbered functions ar dd-numbered ones: 1. f(x) = (x…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Derivatives: using (4 step rule). 4. f(x)=sin3xcos3x 5. f(x)= x² cos(x² +1)

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Q: 1. f(x) = sin x at the point with abscissa x = A. Point of Tangency B. The Gradient of the Tangent…

A: Equation of tangent and normal

Q: uestion-9 a) Using 2nd derivative test, find the absolute extremes of f(x) = x – Vx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: derivative of y=1/b²+bx-aln(a+bx)

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Q: Differentiate the function. Then find an equation of the tangent line at the indicated point on the…

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Q: 25. f(x) = x %3D tive of the function. If possible, identify the derivative function looking at the…

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS. WE ARE ANSWERING FIRST THREE QUESTIONS FOR YOU AS…

Q: Find the instantaneous rate of change of f(x) = x* at x = 3. %3D Find the derivative of g(x) = x + x…

A: 1) Given, f(x)=x2 at x=3 Use the definition of instantaneous rate of change: The instantaneous rate…

Q: 4. у"- Зу' + 2у cos e*

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Q: Equation of the line tangent to the graph of f(x)=(x)(1-2x)^3 at (-1,1).

A: The given function is: f(x)=(x)(1-2x)3 And, at point (1,-1), we have to find the equation of the…

Q: How to find the antiderivative of the given derivative function? a. To find the original function.…

A: The answer is given below in the next step:

Q: Q: Use the Second Derivative Test to classify the local extremes of the function f(x, y) =…

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Q: Applications of Derivative: Tangent and Normal Line 1. For x³ + y³ = 6xy, find the point where…

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